Question

How do you simplify `(x^-2y^2)^-3` and write it using only positive exponents?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule for exponents to eliminate the outer exponent:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(x^color(red)(-2)y^color(red)(2))^color(blue)(-3) = x^(color(red)(-2) xx color(blue)(-3))y^(color(red)(2) xx color(blue)(-3)) = x^6y^-6`

Now, use this rule for exponents to eliminate the negative exponent:

`x^color(red)(a) = 1/x^color(red)(-a)`

`x^6y^color(red)(-6) = x^6/y^color(red)(- -6) = x^6/y^color(red)(6)`